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by Uva@90 » Tue Oct 15, 2013 4:23 am
vipulgoyal wrote:find the reminder when 51^203 is divided by 7 ??
4
Hi,
Check this link,
https://www.beatthegmat.com/screw-these- ... 81931.html(:P I am posting link for your questions,Just Resuing)

Regards,
Uva.
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by theCodeToGMAT » Tue Oct 15, 2013 5:32 am
51^203

51/7 leaves remainder 2

So, rephrase the question to (2)^203/7

Now, we know that 8/7 will leave remainder 1.. Also, we can see that we can reach that by doing 2^3.

So, rewriting the same equation

[(2)^3]^67 * (2)^2
_________________
7

(8)^67 * 4
________
7

= ((1)^67 * 4)/7

= 4/7

So, remainder is "4"
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by ceilidh.erickson » Tue Oct 15, 2013 4:49 pm
This is not the sort of question that you're likely to see on the real GMAT. They often ask about units digits of numbers taken to large exponents, but not about remainders.

Ian Stewart's explanation here is spot-on: https://www.beatthegmat.com/screw-these- ... 81931.html
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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